For one, Foroutan notes that it "can soothe the respiratory tract and digestive tract" (via Shape). It is also considered a prebiotic, which is necessary to maintain healthy gut bacteria. Another reason it is probably considered so attractive to the health community is its versatility. Sea moss can be found in gel, gummy, and powder form and is often used as a thickening agent (via Healthline).
Sea moss doesn't have to be ingested to show off its health benefits. When applied topically as a gel mask, it can act as a defense against acne, as well as help the skin stay hydrated (per the Chicago Tribune).
For as long as sea moss has been around, it may come as a surprise that the research backing its health benefits is still in its beginning stages (via the Chicago Tribune). So, if you want to add this edible plant to your diet, do so gradually to avoid any yet-to-be-discovered side effects.